# Lecture02A - Equations of State How far can we push...

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Lecture 2 1 Equations of State – How far can we push it? (16.3,16.4) Consider the vdW equation of state: ( 29 2 a P V b RT V + - = ( 29 ( 29 2 2 PV a V b RTV + - = 3 2 0 RT a ab V b V V P P P - + + - = ( 29 Cubic equation in V 3 roots ( 29 3 2 0 PV RT bP V aV ab - + + - = Fig. 16.7 Figure shows that below the critical point, liquid and gaseous phase of CO 2 can coexist. c So, at a given T<T , as you compress the gas, (G A) you reach a point where V will change with essentially no increase in P (A D), until all of the gas liquifies. Then, further compression requires a hug e increase in P (D L).

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Lecture 2 2 P vs. V for vdW equation Fig. 16.8a 2 2 At : 0 Inflection point in curve c c c T T P P T V V = = c For T<T undulating curve reflects 3 roots of our cubic equation in V. But at the critical point, T c , the three roots become degenerate: ( 29 3 3 2 2 3 0 3 3 0 c c c c V V V V V V V V - = - + - = 3 2 Equate with 0 RT a ab V b V V P P P - + + - =
Lecture 2 3

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